# CSM_RH Paper 55 v0.1

Campaign 45 structural closure package.

Main results:

- For every fixed 0<kappa<=1:
  `PESC(kappa) <=> beta_* <= 1-kappa/2`.
- Maximal exponent law:
  `kappa_* = 2(1-beta_*)`.
- A fixed explicit-formula zero mode on the seed boundary has lag exponent exactly `delta=kappa`.
- The discrete derivative of a fixed zero mode has `1-O(H/N)` of its Fourier L2 mass in the principal Fejer arc at every sublinear lag.
- The same mode has only `o(1)` cumulative dyadic contraction mass.
- Principal-arc projection/detrending cannot bypass the mode without an independent power bound on the projected coefficient.
- Any strict seeded MLEPG amplifier is automatically a strict zero-strip improvement theorem.
- Campaign 45 amplifier architecture is structurally complete; arithmetic seed and strip-gap gates remain open.
- Candidate next campaign: seeded arithmetic strip-gap generation.

No RH proof is claimed.